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We review the concept of support vector machines (SVMs) and discuss examples of their use. One of the benefits of SVM algorithms, compared with neural networks and decision trees is that they can be less susceptible to over fitting than those other algorithms are to over training. This issue is related to the generalisation of a multivariate algorithm (MVA); a problem that has often been overlooked in particle physics. We discuss cross validation and how this can be used to improve the generalisation of a MVA in the context of High Energy Physics analyses. The examples presented use the Toolkit for Multivariate Analysis (TMVA) based on ROOT and describe our improvements to the SVM functionality and new tools introduced for cross validation within this framework.

A search is reported for pairs of light Higgs bosons ( ) produced in supersymmetric cascade decays in final states with small missing transverse momentum. A data set of LHC collisions collected with the CMS detector at and corresponding to an integrated luminosity of 138 is used. The search targets events where both bosons decay into pairs that are reconstructed as large-radius jets using substructure techniques. No evidence is found for an excess of events beyond the background expectations of the standard model (SM). Results from the search are interpreted in the next-to-minimal supersymmetric extension of the SM, where a \"singlino\" of small mass leads to squark and gluino cascade decays that can predominantly end in a highly Lorentz-boosted singlet-like and a singlino-like neutralino of small transverse momentum. Upper limits are set on the product of the squark or gluino pair production cross section and the square of the branching fraction of the in a benchmark model containing almost mass-degenerate gluinos and light-flavour squarks. Under the assumption of an SM-like branching fraction, bosons with masses in the range 40-120 arising from the decays of squarks or gluinos with a mass of 1200-2500 are excluded at 95% confidence level.

The double differential cross sections of the Drell-Yan lepton pair ( , dielectron or dimuon) production are measured as functions of the invariant mass , transverse momentum , and . The observable, derived from angular measurements of the leptons and highly correlated with , is used to probe the low- region in a complementary way. Dilepton masses up to 1 are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3 of proton-proton collisions recorded with the CMS detector at the LHC at a centre-of-mass energy of 13 . Measurements are compared with predictions based on perturbative quantum chromodynamics, including soft-gluon resummation.

The production of Z bosons associated with jets is measured in collisions at with data recorded with the CMS experiment at the LHC corresponding to an integrated luminosity of 36.3 . The multiplicity of jets with transverse momentum is measured for different regions of the Z boson's , from lower than 10 to higher than 100 . The azimuthal correlation between the Z boson and the leading jet, as well as the correlations between the two leading jets are measured in three regions of . The measurements are compared with several predictions at leading and next-to-leading orders, interfaced with parton showers. Predictions based on transverse-momentum dependent parton distributions and corresponding parton showers give a good description of the measurement in the regions where multiple parton interactions and higher jet multiplicities are not important. The effects of multiple parton interactions are shown to be important to correctly describe the measured spectra in the low regions.

Abstract A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum $$p_{\\textrm{T}}$$ p T . This observable is measured in multijet events over the range of $$p_{\\textrm{T}} = 360$$ p T = 360 – $$3170\\,\\text {Ge}\\hspace{-.08em}\\text {V} $$ 3170 Ge V based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13 $$\\,\\text {Te}\\hspace{-.08em}\\text {V}$$ Te V , corresponding to an integrated luminosity of 134 $$\\,\\text {fb}^{-1}$$ fb - 1 . The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is $$\\alpha _\\textrm{S} (m_{{\\textrm{Z}}}) =0.1177 \\pm 0.0013\\, \\text {(exp)} _{-0.0073}^{+0.0116} \\,\\text {(theo)} = 0.1177_{-0.0074}^{+0.0117}$$ α S ( m Z ) = 0.1177 ± 0.0013 (exp) - 0.0073 + 0.0116 (theo) = 0 . 1177 - 0.0074 + 0.0117 , where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of $$\\alpha _\\textrm{S}$$ α S in the $$\\,\\text {Te}\\hspace{-.08em}\\text {V}$$ Te V region shows no deviation from the expected NLO pQCD behaviour.

Abstract A search for $${\\text {Z}{}{}} {\\text {Z}{}{}} $$ Z Z and $${\\text {Z}{}{}} {\\text {H}{}{}} $$ Z H production in the $${\\text {b}{}{}} {\\bar{{\\text {b}{}{}}}{}{}} {\\text {b}{}{}} {\\bar{{\\text {b}{}{}}}{}{}} $$ b b ¯ b b ¯ final state is presented, where H is the standard model (SM) Higgs boson. The search uses an event sample of proton-proton collisions corresponding to an integrated luminosity of 133 $$\\,\\text {fb}^{-1}$$ fb - 1 collected at a center-of-mass energy of 13 $$\\,\\text {Te}\\hspace{-.08em}\\text {V}$$ Te V with the CMS detector at the CERN LHC. The analysis introduces several novel techniques for deriving and validating a multi-dimensional background model based on control samples in data. A multiclass multivariate classifier customized for the $${\\text {b}{}{}} {\\bar{{\\text {b}{}{}}}{}{}} {\\text {b}{}{}} {\\bar{{\\text {b}{}{}}}{}{}} $$ b b ¯ b b ¯ final state is developed to derive the background model and extract the signal. The data are found to be consistent, within uncertainties, with the SM predictions. The observed (expected) upper limits at 95% confidence level are found to be 3.8 (3.8) and 5.0 (2.9) times the SM prediction for the $${\\text {Z}{}{}} {\\text {Z}{}{}} $$ Z Z and $${\\text {Z}{}{}} {\\text {H}{}{}} $$ Z H production cross sections, respectively.

Abstract The production of Z bosons associated with jets is measured in $$\\text {p}\\text {p}$$ pp collisions at $$\\sqrt{s}=13\\,\\text {Te}\\hspace{-.08em}\\text {V} $$ s = 13 Te V with data recorded with the CMS experiment at the LHC corresponding to an integrated luminosity of 36.3 $$\\,\\text {fb}^{-1}$$ fb - 1 . The multiplicity of jets with transverse momentum $$p_{\\textrm{T}} > 30\\,\\text {Ge}\\hspace{-.08em}\\text {V} $$ p T > 30 Ge V is measured for different regions of the Z boson’s $$p_{\\textrm{T}} (\\text {Z })$$ p T ( Z ) , from lower than 10 $$\\,\\text {Ge}\\hspace{-.08em}\\text {V}$$ Ge V to higher than 100 $$\\,\\text {Ge}\\hspace{-.08em}\\text {V}$$ Ge V . The azimuthal correlation $$\\varDelta \\phi $$ Δ ϕ between the Z boson and the leading jet, as well as the correlations between the two leading jets are measured in three regions of $$p_{\\textrm{T}} (\\text {Z })$$ p T ( Z ) . The measurements are compared with several predictions at leading and next-to-leading orders, interfaced with parton showers. Predictions based on transverse-momentum dependent parton distributions and corresponding parton showers give a good description of the measurement in the regions where multiple parton interactions and higher jet multiplicities are not important. The effects of multiple parton interactions are shown to be important to correctly describe the measured spectra in the low $$p_{\\textrm{T}} (\\text {Z })$$ p T ( Z ) regions.

Abstract Results are presented from a search for CP violation in top quark pair production, using proton-proton collisions at a center-of-mass energy of 13 TeV. The data used for this analysis consist of final states with two charged leptons collected by the CMS experiment, and correspond to an integrated luminosity of 35.9 fb −1. The search uses two observables, O $$ \\mathcal{O} $$ 1 and O $$ \\mathcal{O} $$ 3, which are Lorentz scalars. The observable O $$ \\mathcal{O} $$ 1 is constructed from the four-momenta of the charged leptons and the reconstructed top quarks, while O $$ \\mathcal{O} $$ 3 consists of the four-momenta of the charged leptons and the b quarks originating from the top quarks. Asymmetries in these observables are sensitive to CP violation, and their measurement is used to determine the chromoelectric dipole moment of the top quark. The results are consistent with the expectation from the standard model.

Abstract A search is reported for heavy resonances and quantum black holes decaying into eμ, eτ, and μτ final states in proton-proton collision data recorded by the CMS experiment at the CERN LHC during 2016–2018 at s $$ \\sqrt{s} $$ = 13 TeV, corresponding to an integrated luminosity of 138 fb −1. The eμ, eτ, and μτ invariant mass spectra are reconstructed, and no evidence is found for physics beyond the standard model. Upper limits are set at 95% confidence level on the product of the cross section and branching fraction for lepton flavor violating signals. Three benchmark signals are studied: resonant τ sneutrino production in R parity violating supersymmetric models, heavy Z′ gauge bosons with lepton flavor violating decays, and nonresonant quantum black hole production in models with extra spatial dimensions. Resonant τ sneutrinos are excluded for masses up to 4.2TeV in the eμ channel, 3.7TeV in the eτ channel, and 3.6TeV in the μτ channel. A Z′ boson with lepton flavor violating couplings is excluded up to a mass of 5.0TeV in the eμ channel, up to 4.3Te V in the eτ channel, and up to 4.1TeV in the μτ channel. Quantum black holes in the benchmark model are excluded up to the threshold mass of 5.6TeV in the eμ channel, 5.2TeV in the eτ channel, and 5.0TeV in the μτ channel. In addition, model-independent limits are extracted to allow comparisons with other models for the same final states and similar event selection requirements. The results of these searches provide the most stringent limits available from collider experiments for heavy particles that undergo lepton flavor violating decays.

A measurement of the $ZZ$ production in the $\\ell^{-}\\ell^{+}\\ell^{\\prime -}\\ell^{\\prime +}$ and $\\ell^{-}\\ell^{+}\\nu\\bar{\\nu}$ channels $(\\ell = e, \\mu)$ in proton--proton collisions at $\\sqrt{s} = 8$ TeV at the Large Hadron Collider at CERN, using data corresponding to an integrated luminosity of 20.3 fb$^{-1}$ collected by the ATLAS experiment in 2012 is presented. The fiducial cross sections for $ZZ\\to\\ell^{-}\\ell^{+}\\ell^{\\prime -}\\ell^{\\prime +}$ and $ZZ\\to \\ell^{-}\\ell^{+}\\nu\\bar{\\nu}$ are measured in selected phase-space regions. The total cross section for $ZZ$ events produced with both $Z$ bosons in the mass range 66 to 116 GeV is measured from the combination of the two channels to be $7.3\\pm0.4\\textrm{(stat)}\\pm0.3\\textrm{(syst)}\\pm0.2\\textrm{(lumi)}$ pb, which is consistent with the Standard Model prediction of $6.6^{+0.7}_{-0.6}$ pb. The differential cross sections in bins of various kinematic variables are presented. The differential event yield as a function of the transverse momentum of the leading $Z$ boson is used to set limits on anomalous neutral triple gauge boson couplings in $ZZ$ production.